Publications associées à Safe and Sophie Germain primes

Non-planarity of Markoff graphs mod p

We prove the non-planarity of a family of 3-regular graphs constructed from the solutions to the Markoff equation x2 + y2 + z2 = xyz modulo prime numbers greater than 7. The proof uses Euler characteristic and an enumeration of the short cycles in these gr ...

European Mathematical Soc-Ems2024

Toroidal families and averages of L-functions, I

Philippe Michel

We initiate the study of certain families of L-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values L( 2 1 , chi a )L( 21 , chi b ) for arbitrary ...

Polish Acad Sciences Inst Mathematics-Impan2024

ALGEBRAIC TWISTS OF GL3 x GL2 L-FUNCTIONS

Philippe Michel, Yongxiao Lin

We prove that the coefficients of a GL3 x GL2 Rankin-Selberg L-function do not correlate with a wide class of trace functions of small conductor modulo primes, generalizing the corresponding result of Fouvry, Kowalski, and Michel for GL2 and of Kowalski, L ...

Johns Hopkins Univ Press2023

Experiments with the Markoff Surface

Matthew De Courcy-Ireland, Sandy Lee

We confirm, for the primes up to 3000, the conjecture of Bourgain-Gamburd-Sarnak and Baragar on strong approximation for the Markoff surface modulo primes. For primes congruent to 3 modulo 4, we find data suggesting that some natural graphs constructed fro ...

TAYLOR & FRANCIS INC2022

Generalized Norm-compatible Systems on Unitary Shimura Varieties

Mohamed Réda Boumasmoud

We define and study in terms of integral Iwahoriâ Hecke algebras a new class of geometric operators acting on the Bruhat-Tits building of connected reductive groups over p-adic fields. These operators, which we call U-operators, generalize the geometric n ...

EPFL2019

Some applications of smooth bilinear forms with Kloosterman sums

Philippe Michel

We revisit a recent bound of I. Shparlinski and T. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms. We use these bounds to improve on earlier resul ...

Maik Nauka/Interperiodica/Springer2017

On Moments Of Twisted L-Functions

Philippe Michel

We study the average of the product of the central values of two L-functions of modular forms f and g twisted by Dirichlet characters to a large prime modulus q. As our principal tools, we use spectral theory to develop bounds on averages of shifted convol ...

Johns Hopkins Univ Press2017

Computational Aspects of Jacobians of Hyperelliptic Curves

Alina Dudeanu

Nowadays, one area of research in cryptanalysis is solving the Discrete Logarithm Problem (DLP) in finite groups whose group representation is not yet exploited. For such groups, the best one can do is using a generic method to attack the DLP, the fastest ...

EPFL2016

Sign changes of Kloosterman sums with almost prime moduli

Ping Xi

We prove that the Kloosterman sum changes sign infinitely often as runs over squarefree moduli with at most 10 prime factors, which improves the previous results of Fouvry and Michel, Sivak-Fischler and Matomaki, replacing 10 by 23, 18 and 15, respectively ...

Springer Verlag2015

On The Exponent Of Distribution Of The Ternary Divisor Function

Philippe Michel

We show that the exponent of distribution of the ternary divisor function d(3) in arithmetic progressions to prime moduli is at least 1/2 + 1/46, improving results of Friedlander-Iwaniec and Heath-Brown. Furthermore, when averaging over a fixed residue cla ...

London Mathematical Society, Cambridge2015